The mathematical model and numerical simulations of the solidification of a cylindrical shaped casting, which take into account the process of filling the mould cavity by liquid metal and feeding the casting through the riser during its solidification, are presented in the paper. Mutual dependence of thermal and flow phenomena were taken into account because have an essential influence on solidification process. The effect of the riser shape on the effectiveness of feeding of the solidifying casting was determined. In order to obtain the casting without shrinkage defects, an appropriate selection of riser shape was made, which is important for foundry practice. Numerical calculations of the solidification process of system consisting of the casting and the conical or cylindrical riser were carried out. The velocity fields have been obtained from the solution of momentum equations and continuity equation, while temperature fields from solving the equation of heat conductivity containing the convection term. Changes in thermo-physical parameters as a function of temperature were considered. The finite element method (FEM) was used to solve the problem.
The paper presents an approach of numerical modelling of alloy solidification in permanent mold and transient heat transport between the casting and the mold in two-dimensional space. The gap of time-dependent width called "air gap", filled with heat conducting gaseous medium is included in the model. The coefficient of thermal conductivity of the gas filling the space between the casting and the mold is small enough to introduce significant thermal resistance into the heat transport process. The mathematical model of heat transport is based on the partial differential equation of heat conduction written independently for the solidifying region and the mold. Appropriate solidification model based on the latent heat of solidification is also included in the mathematical description. These equations are supplemented by appropriate initial and boundary conditions. The formation process of air gap depends on the thermal deformations of the mold and the casting. The numerical model is based on the finite element method (FEM) with independent spatial discretization of interacting regions. It results in multi-mesh problem because the considered regions are disconnected.
In this paper, the mathematical model and numerical simulations of the molten steel flow by the submerged entry nozzle and the filling process of the continuous casting mould cavity are presented. In the mathematical model, the temperature fields were obtained by solving the energy equation, while the velocity fields were calculated by solving the momentum equations and the continuity equation. These equations contain the turbulent viscosity which is found by solving two additional transport equations for the turbulent kinetic energy and its rate of dissipation. In the numerical simulations, coupling of the thermal and fluid flow phenomena by changes in the thermophysical parameters of alloy depending on the temperature has been taken into consideration. This problem (2D) was solved by using the finite element method. Numerical simulations of filling the continuous casting mould cavity were performed for two variants of liquid metal pouring. The effect of the cases of pouring the continuous casting mould on the velocity fields and the solid phase growth kinetics in the process of filling the continuous casting mould was evaluated as these magnitudes have an influence on the high quality of the continuous cast steel slab.